Abstract
The (Nörlund) logarithmic means of the Fourier series of the integrable function f is:
In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh–Fourier series of functions in the uniform, and in the L1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm.
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The first author is supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. M 36511/2001, T 048780, and by the Széchenyi fellowship of the Hungarian Ministry of Education Szö 184/2003
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Gát, G., Goginava, U. Uniform and L–convergence of Logarithmic Means of Walsh–Fourier Series. Acta Math Sinica 22, 497–506 (2006). https://doi.org/10.1007/s10114-005-0648-8
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DOI: https://doi.org/10.1007/s10114-005-0648-8